An Application of Neutrosophic Set to Relative Importance Assignment in AHP
The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of whi...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/20/2636 |
| _version_ | 1797513975644028928 |
|---|---|
| author | Napat Harnpornchai Wiriyaporn Wonggattaleekam |
| author_facet | Napat Harnpornchai Wiriyaporn Wonggattaleekam |
| author_sort | Napat Harnpornchai |
| collection | DOAJ |
| description | The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market. |
| first_indexed | 2024-03-10T06:25:07Z |
| format | Article |
| id | doaj.art-9af13d71eb5a4a189d8689f244805b6b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:25:07Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9af13d71eb5a4a189d8689f244805b6b2023-11-22T19:03:01ZengMDPI AGMathematics2227-73902021-10-01920263610.3390/math9202636An Application of Neutrosophic Set to Relative Importance Assignment in AHPNapat Harnpornchai0Wiriyaporn Wonggattaleekam1Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Agricultural Economy and Development, Faculty of Agriculture, Chiang Mai University, Chiang Mai 50200, ThailandThe paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market.https://www.mdpi.com/2227-7390/9/20/2636fuzzy and neutrosophic AHPneutrosophic setrelative importance assignmentdiscrete single valued neutrosophic number (DSVNN)deneutrosophicationsimilarity measure |
| spellingShingle | Napat Harnpornchai Wiriyaporn Wonggattaleekam An Application of Neutrosophic Set to Relative Importance Assignment in AHP Mathematics fuzzy and neutrosophic AHP neutrosophic set relative importance assignment discrete single valued neutrosophic number (DSVNN) deneutrosophication similarity measure |
| title | An Application of Neutrosophic Set to Relative Importance Assignment in AHP |
| title_full | An Application of Neutrosophic Set to Relative Importance Assignment in AHP |
| title_fullStr | An Application of Neutrosophic Set to Relative Importance Assignment in AHP |
| title_full_unstemmed | An Application of Neutrosophic Set to Relative Importance Assignment in AHP |
| title_short | An Application of Neutrosophic Set to Relative Importance Assignment in AHP |
| title_sort | application of neutrosophic set to relative importance assignment in ahp |
| topic | fuzzy and neutrosophic AHP neutrosophic set relative importance assignment discrete single valued neutrosophic number (DSVNN) deneutrosophication similarity measure |
| url | https://www.mdpi.com/2227-7390/9/20/2636 |
| work_keys_str_mv | AT napatharnpornchai anapplicationofneutrosophicsettorelativeimportanceassignmentinahp AT wiriyapornwonggattaleekam anapplicationofneutrosophicsettorelativeimportanceassignmentinahp AT napatharnpornchai applicationofneutrosophicsettorelativeimportanceassignmentinahp AT wiriyapornwonggattaleekam applicationofneutrosophicsettorelativeimportanceassignmentinahp |